Ë
    qwjëI  ã                   óv  — d dl Z d dlZd dlmZ d dlmZ d dlmZ d dl	m
Z d dlmZmZmZmZmZmZmZ g d¢Z G d„ d	e«      Zd
„ Z G d„ de«      Z G d„ de«      Z G d„ de«      Z G d„ de«      Z G d„ de«      Z G d„ de«      Ze j:                  e   j>                  Z eD ]  Z! ee e!   «      e e!   _"        Œ y)é    N)Úinf)Úarray_api_extra)Úspecial)Ú_ufuncs)ÚContinuousDistributionÚDiscreteDistributionÚ_RealIntervalÚ_IntegerIntervalÚ_RealParameterÚ_ParameterizationÚ_combine_docs)ÚNormalÚLogisticÚUniformÚBinomialc                   óÚ  ‡ — e Zd ZdZ ee ef¬«      Z edef¬«      Z ee ef¬«      Z e	dded¬«      Z
 e	dd	ed
¬«      Z e	ded¬«      Z ee
e«      gZeZd ej"                  dej$                  z  «      z  Z ej(                  dej$                  z  «      dz  Zd%ˆ fd„	Zdddœˆ fd„
Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z d„ Z!d„ Z"d„ Z#d „ Z$d!„ Z%d"„ Z&ddge&_'        d#„ Z(d$„ Z)ˆ xZ*S )&r   a  Normal distribution with prescribed mean and standard deviation.

    The probability density function of the normal distribution is:

    .. math::

        f(x) = \frac{1}{\sigma \sqrt{2 \pi}} \exp {
            \left( -\frac{1}{2}\left( \frac{x - \mu}{\sigma} \right)^2 \right)}

    ©Ú	endpointsr   Úmuz\mu)éÿÿÿÿé   ©ÚsymbolÚdomainÚtypicalÚsigmaz\sigma)ç      à?g      ø?Úx©r   r   r   é   c                 óP   •— |€|€t         ‰| �  t        «      S t         ‰| �  | «      S ©N)ÚsuperÚ__new__ÚStandardNormal)Úclsr   r   ÚkwargsÚ	__class__s       €úc/var/www/html/newmanjeet/manjet/venv/lib/python3.12/site-packages/scipy/stats/_new_distributions.pyr$   zNormal.__new__.   s*   ø€ Øˆ:˜%˜-Ü‘7‘?¤>Ó2Ð2Ü‰w‰˜sÓ#Ð#ó    ç        ç      ð?©r   r   c                ó*   •— t        ‰| �  d||dœ|¤Ž y )Nr-   © ©r#   Ú__init__)Úselfr   r   r'   r(   s       €r)   r1   zNormal.__init__3   s   ø€ Ü‰ÑÐ6˜B eÑ6¨vÓ6r*   c                óf   — t         j                  | ||z
  |z  «      t        j                  |«      z
  S r"   )r%   Ú_logpdf_formulaÚnpÚlog©r2   r   r   r   r'   s        r)   r4   zNormal._logpdf_formula6   s*   € Ü×-Ñ-¨d°Q¸±V¸U±NÓCÄbÇfÁfÈUÃmÑSÐSr*   c                ó@   — t         j                  | ||z
  |z  «      |z  S r"   )r%   Ú_pdf_formular7   s        r)   r9   zNormal._pdf_formula9   s"   € Ü×*Ñ*¨4°!°b±&¸%±Ó@À5ÑHÐHr*   c                ó:   — t         j                  | ||z
  |z  «      S r"   )r%   Ú_logcdf_formular7   s        r)   r;   zNormal._logcdf_formula<   s   € Ü×-Ñ-¨d°Q¸±V¸U±NÓCÐCr*   c                ó:   — t         j                  | ||z
  |z  «      S r"   )r%   Ú_cdf_formular7   s        r)   r=   zNormal._cdf_formula?   s   € Ü×*Ñ*¨4°!°b±&¸%±Ó@Ð@r*   c                ó:   — t         j                  | ||z
  |z  «      S r"   )r%   Ú_logccdf_formular7   s        r)   r?   zNormal._logccdf_formulaB   s   € Ü×.Ñ.¨t°a¸"±f¸e±^ÓDÐDr*   c                ó:   — t         j                  | ||z
  |z  «      S r"   )r%   Ú_ccdf_formular7   s        r)   rA   zNormal._ccdf_formulaE   s   € Ü×+Ñ+¨D°1°r±6¸5±.ÓAÐAr*   c                ó:   — t         j                  | |«      |z  |z   S r"   )r%   Ú_icdf_formular7   s        r)   rC   zNormal._icdf_formulaH   s   € Ü×+Ñ+¨D°!Ó4°uÑ<¸rÑAÐAr*   c                ó:   — t         j                  | |«      |z  |z   S r"   )r%   Ú_ilogcdf_formular7   s        r)   rE   zNormal._ilogcdf_formulaK   s   € Ü×.Ñ.¨t°QÓ7¸%Ñ?À"ÑDÐDr*   c                ó:   — t         j                  | |«      |z  |z   S r"   )r%   Ú_iccdf_formular7   s        r)   rG   zNormal._iccdf_formulaN   s   € Ü×,Ñ,¨T°1Ó5¸Ñ=ÀÑBÐBr*   c                ó:   — t         j                  | |«      |z  |z   S r"   )r%   Ú_ilogccdf_formular7   s        r)   rI   zNormal._ilogccdf_formulaQ   s   € Ü×/Ñ/°°aÓ8¸5Ñ@À2ÑEÐEr*   c                ój   — t         j                  | «      t        j                  t	        |«      «      z   S r"   )r%   Ú_entropy_formular5   r6   Úabs©r2   r   r   r'   s       r)   rK   zNormal._entropy_formulaT   s%   € Ü×.Ñ.¨tÓ4´r·v±v¼cÀ%»jÓ7IÑIÐIr*   c                ó@  — t         j                  | «      }t        j                  d¬«      5  t        j                  t        j                  t        |«      «      dz   «      }d d d «       t        j                  t        j                  |«      d¬«      S # 1 sw Y   Œ4xY w)NÚignore©Údividey                r   ©Úaxis)	r%   Ú_logentropy_formular5   Úerrstater6   rL   r   Ú	logsumexpÚbroadcast_arrays)r2   r   r   r'   ÚlH0Úllss         r)   rT   zNormal._logentropy_formulaW   sp   € Ü×0Ñ0°Ó6ˆÜ�[‰[ Ö)ô —&‘&œŸ™¤ E£
Ó+¨BÑ.Ó/ˆC÷ *ô × Ñ ¤×!4Ñ!4°S¸#Ó!>ÀQÔGÐG÷	 *Ð)ús   ¬5BÂBc                ó   — |S r"   r/   rM   s       r)   Ú_median_formulazNormal._median_formula_   ó   € Øˆ	r*   c                ó   — |S r"   r/   rM   s       r)   Ú_mode_formulazNormal._mode_formulab   r\   r*   c                óF   — |dk(  rt        j                  |«      S |dk(  r|S y )Nr   r   )r5   Ú	ones_like©r2   Úorderr   r   r'   s        r)   Ú_moment_raw_formulazNormal._moment_raw_formulae   s'   € Ø�AŠ:Ü—<‘< Ó#Ð#Ø�aŠZØˆIàr*   c                ó¼   — |dk(  rt        j                  |«      S |dz  rt        j                  |«      S ||z  t        j                  t        |«      dz
  d¬«      z  S )Nr   r    r   T)Úexact)r5   r`   Ú
zeros_liker   Ú
factorial2Úintra   s        r)   Ú_moment_central_formulazNormal._moment_central_formulan   sT   € Ø�AŠ:Ü—<‘< Ó#Ð#Ø�QŠYÜ—=‘= Ó$Ð$ð ˜%‘<¤'×"4Ñ"4´S¸³ZÀ!±^È4Ô"PÑPÐPr*   c                ó0   — |j                  |||¬«      d   S )N)ÚlocÚscaleÚsizer/   ©Únormal)r2   Ú
full_shapeÚrngr   r   r'   s         r)   Ú_sample_formulazNormal._sample_formulaw   s   € Ø�z‰z˜b¨°JˆzÓ?ÀÑCÐCr*   )NN)+Ú__name__Ú
__module__Ú__qualname__Ú__doc__r	   r   Ú
_mu_domainÚ_sigma_domainÚ
_x_supportr   Ú	_mu_paramÚ_sigma_paramÚ_x_paramr   Ú_parameterizationsÚ	_variabler5   ÚsqrtÚpiÚ_normalizationr6   Ú_log_normalizationr$   r1   r4   r9   r;   r=   r?   rA   rC   rE   rG   rI   rK   rT   r[   r^   rc   Úordersri   rr   Ú__classcell__©r(   s   @r)   r   r      s>  ø„ ñ	ñ ¨3¨$°¨Ô5€JÙ!¨Q°¨HÔ5€MÙ¨3¨$°¨Ô5€Já˜t¨V¸JØ'.ô0€Iá! '°)ÀMØ*4ô6€Lá˜c¨*¸gÔF€Há+¨I°|ÓDÐEÐà€IØ�w�r—w‘w˜q §¡™wÓ'Ñ'€NØ˜Ÿ™  "§%¡%¡›¨Ñ*Ðõ$ð
   rö 7òTòIòDòAòEòBòBòEòCòFòJòHòòòð #$ Q ÐÔòQöDr*   r   c                 ó\   — t        j                  | |t        j                  dz  z   gd¬«      S )Ny              ð?r   rR   )r   rV   r5   r€   )Úlog_pÚlog_qs     r)   Ú	_log_diffr‰   {   s&   € Ü×Ñ˜e U¬2¯5©5°©8¡^Ð4¸1Ô=Ð=r*   c                   óˆ  — e Zd ZdZ ee ef¬«      Z eded¬«      ZeZ	g Z
d ej                  dej                  z  «      z  Z ej                  dej                  z  «      dz  Z ej"                  d«      Z ej"                  d	«      Zd
„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z d„ Z!d„ Z"d„ Z#d„ Z$d„ Z%d„ Z&y)r%   zÌStandard normal distribution.

    The probability density function of the standard normal distribution is:

    .. math::

        f(x) = \frac{1}{\sqrt{2 \pi}} \exp \left( -\frac{1}{2} x^2 \right)

    r   r   )éûÿÿÿé   r   r   r    r+   r,   c                 ó0   — t        j                  | fi |¤Ž y r"   )r   r1   ©r2   r'   s     r)   r1   zStandardNormal.__init__’   s   € Ü×'Ñ'¨Ñ7°Ó7r*   c                 ó.   — | j                   |dz  dz  z    S ©Nr    )r‚   ©r2   r   r'   s      r)   r4   zStandardNormal._logpdf_formula•   s   € Ø×(Ñ(¨1¨a©4°©6Ñ1Ð2Ð2r*   c                 óT   — | j                   t        j                  |dz   dz  «      z  S r�   )r�   r5   Úexpr‘   s      r)   r9   zStandardNormal._pdf_formula˜   s%   € Ø×"Ñ"¤R§V¡V¨Q°©T¨E°!©G£_Ñ4Ð4r*   c                 ó,   — t        j                  |«      S r"   ©r   Úlog_ndtrr‘   s      r)   r;   zStandardNormal._logcdf_formula›   s   € Ü×Ñ Ó"Ð"r*   c                 ó,   — t        j                  |«      S r"   ©r   Úndtrr‘   s      r)   r=   zStandardNormal._cdf_formulaž   s   € Ü�|‰|˜A‹Ðr*   c                 ó.   — t        j                  | «      S r"   r•   r‘   s      r)   r?   zStandardNormal._logccdf_formula¡   s   € Ü×Ñ  Ó#Ð#r*   c                 ó.   — t        j                  | «      S r"   r˜   r‘   s      r)   rA   zStandardNormal._ccdf_formula¤   s   € Ü�|‰|˜Q˜BÓÐr*   c                 ó,   — t        j                  |«      S r"   ©r   Úndtrir‘   s      r)   rC   zStandardNormal._icdf_formula§   ó   € Ü�}‰}˜QÓÐr*   c                 ó,   — t        j                  |«      S r"   ©r   Ú	ndtri_expr‘   s      r)   rE   zStandardNormal._ilogcdf_formulaª   ó   € Ü× Ñ  Ó#Ð#r*   c                 ó.   — t        j                  |«       S r"   r�   r‘   s      r)   rG   zStandardNormal._iccdf_formula­   ó   € Ü—‘˜aÓ Ð Ð r*   c                 ó.   — t        j                  |«       S r"   r¡   r‘   s      r)   rI   z StandardNormal._ilogccdf_formula°   s   € Ü×!Ñ! !Ó$Ð$Ð$r*   c                 óZ   — dt        j                  dt         j                  z  «      z   dz  S ©Nr   r    )r5   r6   r€   rŽ   s     r)   rK   zStandardNormal._entropy_formula³   s"   € Ø”B—F‘F˜1œRŸU™U™7“OÑ# QÑ&Ð&r*   c                 ó    — t        j                  t        j                  dt         j                  z  «      «      t        j                  d«      z
  S r�   )r5   Úlog1pr6   r€   rŽ   s     r)   rT   z"StandardNormal._logentropy_formula¶   s.   € Ü�x‰xœŸ™˜q¤§¡™w›Ó(¬2¯6©6°!«9Ñ4Ð4r*   c                  ó   — y©Nr   r/   rŽ   s     r)   r[   zStandardNormal._median_formula¹   ó   € Ør*   c                  ó   — yr¬   r/   rŽ   s     r)   r^   zStandardNormal._mode_formula¼   r­   r*   c                 ó8   — dddddddœ}|j                  |d «      S )Nr   r   é   )r   r   r    r°   é   rŒ   )Úget)r2   rb   r'   Úraw_momentss       r)   rc   z"StandardNormal._moment_raw_formula¿   s%   € Ø  a¨A°!¸Ñ:ˆØ�‰˜u dÓ+Ð+r*   c                 ó(   —  | j                   |fi |¤ŽS r"   ©rc   ©r2   rb   r'   s      r)   ri   z&StandardNormal._moment_central_formulaÃ   ó   € Ø'ˆt×'Ñ'¨Ñ8°Ñ8Ð8r*   c                 ó(   —  | j                   |fi |¤ŽS r"   rµ   r¶   s      r)   Ú_moment_standardized_formulaz+StandardNormal._moment_standardized_formulaÆ   r·   r*   c                 ó,   — |j                  |¬«      d   S ©N©rm   r/   rn   ©r2   rp   rq   r'   s       r)   rr   zStandardNormal._sample_formulaÉ   s   € Ø�z‰z˜zˆzÓ*¨2Ñ.Ð.r*   N)'rs   rt   ru   rv   r	   r   ry   r   r|   r~   r}   r5   r   r€   r�   r6   r‚   Úfloat64r   r   r1   r4   r9   r;   r=   r?   rA   rC   rE   rG   rI   rK   rT   r[   r^   rc   ri   r¹   rr   r/   r*   r)   r%   r%      sé   „ ññ ¨3¨$°¨Ô5€JÙ˜c¨*¸gÔF€HØ€IØÐØ�w�r—w‘w˜q §¡™wÓ'Ñ'€NØ˜Ÿ™  "§%¡%¡›¨Ñ*ÐØ	ˆ�‰�B‹€BØˆB�J‰J�r‹N€Eò8ò3ò5ò#òò$ò ò ò$ò!ò%ò'ò5òòò,ò9ò9ó/r*   r%   c                   óä   — e Zd ZdZ ee ef¬«      Z eded¬«      xZZ	dZ
ej                   ej                  d«      z  Zd„ Zd	„ Zd
„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zy)r   zÆStandard logistic distribution.

    The probability density function of the standard logistic distribution is:

    .. math::

        f(x) = \frac{1}{\left( e^{x / 2} + e^{-x / 2} \right)^2}

    r   r   )i÷ÿÿÿé	   r   r/   r°   c                 óŠ   — t        j                  |«       }|dt        j                  t        j                  |«      «      z  z
  S r�   )r5   rL   r   rª   r“   )r2   r   r'   Úys       r)   r4   zLogistic._logpdf_formulaÝ   s2   € Ü�V‰V�A‹YˆJˆØ�1”w—}‘}¤R§V¡V¨A£YÓ/Ñ/Ñ/Ð/r*   c                 ó>   — dt        j                  |dz  «      z  dz  S )Nr   r    )r5   Úcoshr‘   s      r)   r9   zLogistic._pdf_formulaá   s   € à”R—W‘W˜Q ™U“^Ñ# aÑ'Ð'r*   c                 ó,   — t        j                  |«      S r"   ©r   Ú	log_expitr‘   s      r)   r;   zLogistic._logcdf_formulaå   r£   r*   c                 ó,   — t        j                  |«      S r"   ©r   Úexpitr‘   s      r)   r=   zLogistic._cdf_formulaè   rŸ   r*   c                 ó.   — t        j                  | «      S r"   rÆ   r‘   s      r)   r?   zLogistic._logccdf_formulaë   s   € Ü× Ñ  ! Ó$Ð$r*   c                 ó.   — t        j                  | «      S r"   rÉ   r‘   s      r)   rA   zLogistic._ccdf_formulaî   s   € Ü�}‰}˜a˜RÓ Ð r*   c                 ó,   — t        j                  |«      S r"   ©r   Úlogitr‘   s      r)   rC   zLogistic._icdf_formulañ   rŸ   r*   c                 ó.   — t        j                  |«       S r"   rÎ   r‘   s      r)   rG   zLogistic._iccdf_formulaô   r¥   r*   c                  ó   — y)Ng       @r/   rŽ   s     r)   rK   zLogistic._entropy_formula÷   s   € Ør*   c                 ó,   — t        j                  d«      S r�   ©r5   r6   rŽ   s     r)   rT   zLogistic._logentropy_formulaú   s   € Ü�v‰v�a‹yÐr*   c                  ó   — yr¬   r/   rŽ   s     r)   r[   zLogistic._median_formulaý   r­   r*   c                  ó   — yr¬   r/   rŽ   s     r)   r^   zLogistic._mode_formula   r­   r*   c           	      ó²   — t        |«      }|dz  ryt        j                  |z  t        d|z  dz
  t	        t        j                  |«      d   «      z  «      z  S )Nr    r+   r   )rh   r5   r€   rL   Úfloatr   Ú	bernoulli)r2   rb   r'   Úns       r)   rc   zLogistic._moment_raw_formula  sO   € Ü�‹JˆØˆqŠ5ØÜ�u‰u�a‰xœ#˜q !™t a™x¬5´×1BÑ1BÀ1Ó1EÀbÑ1IÓ+JÑJÓKÑKÐKr*   c                 ó(   —  | j                   |fi |¤ŽS r"   rµ   r¶   s      r)   ri   z Logistic._moment_central_formula	  r·   r*   c                 óH   —  | j                   |fi |¤Ž| j                  |z  z  S r"   )rc   Ú_scaler¶   s      r)   r¹   z%Logistic._moment_standardized_formula  s(   € Ø'ˆt×'Ñ'¨Ñ8°Ñ8¸4¿;¹;ÈÑ;MÑMÐMr*   c                 ó,   — |j                  |¬«      d   S r»   )Úlogisticr½   s       r)   rr   zLogistic._sample_formula  s   € Ø�|‰| ˆ|Ó,¨RÑ0Ð0r*   N)rs   rt   ru   rv   r	   r   ry   r   r~   r|   r}   r5   r€   r   rÜ   r4   r9   r;   r=   r?   rA   rC   rG   rK   rT   r[   r^   rc   ri   r¹   rr   r/   r*   r)   r   r   Í   sœ   „ ññ ¨3¨$°¨Ô5€JÙ)¨#°jÈ'ÔRÐR€I�ØÐà�U‰U�W�R—W‘W˜Q“ZÑ€Fò0ò(ò$ò ò%ò!ò ò!òòòòòLò9òNó1r*   r   c                   ó²  ‡ — e Zd ZdZ edef¬«      Z edef¬«      Z ee ef¬«      Z edef¬«      Z	 edd¬«      Z
 eded	¬
«      Z eded¬
«      Z edded¬«      Z edde	d¬«      Z ede
d¬
«      Zej#                  e«       e	j#                  e«       e
j#                  ee«        eee«       eee«      gZeZdddddœˆ fd„
Zdd„Zd„ Zd„ Zˆ xZS )Ú_LogUniformaª  Log-uniform distribution.

    The probability density function of the log-uniform distribution is:

    .. math::

        f(x; a, b) = \frac{1}
                          {x (\log(b) - \log(a))}

    If :math:`\log(X)` is a random variable that follows a uniform distribution
    between :math:`\log(a)` and :math:`\log(b)`, then :math:`X` is log-uniformly
    distributed with shape parameters :math:`a` and :math:`b`.

    r   r   ÚaÚlog_a©rá   Úb©TT©r   Ú	inclusive©gü©ñÒMbP?gÍÌÌÌÌÌì?r   rä   ©gš™™™™™ñ?g     @�@z\log(a))éýÿÿÿgš™™™™™¹¿r   Úlog_bz\log(b))çš™™™™™¹?r°   r   N©rá   rä   râ   rë   c                ó.   •— t        ‰| �  d||||dœ|¤Ž y )Nrí   r/   r0   )r2   rá   rä   râ   rë   r'   r(   s         €r)   r1   z_LogUniform.__init__:  s   ø€ Ü‰ÑÐF˜1 ¨°eÑF¸vÓFr*   c                 ó
  — |€t        j                  |«      n|}|€t        j                  |«      n|}|€t        j                  |«      n|}|€t        j                  |«      n|}|j                  t	        ||||¬«      «       |S )Nrí   )r5   r“   r6   ÚupdateÚdict)r2   rá   rä   râ   rë   r'   s         r)   Ú_process_parametersz_LogUniform._process_parameters=  sj   € Ø˜YŒB�F‰F�5ŒM¨AˆØ˜YŒB�F‰F�5ŒM¨AˆØ"˜]”—‘�q”	°ˆØ"˜]”—‘�q”	°ˆØ�‰”d˜Q !¨5¸Ô>Ô?Øˆr*   c                ó   — ||z
  |z  dz  S )Nr   r/   )r2   r   râ   rë   r'   s        r)   r9   z_LogUniform._pdf_formulaH  s   € Ø˜‘ Ñ! BÑ&Ð&r*   c           	      óÈ   — |dk(  r| j                   S | j                   ||z
  z  |z  }t        j                  t        j                  t	        ||z  ||z  «      «      «      }||z  S r¬   )Ú_oner5   Úrealr“   r‰   )r2   rb   râ   rë   r'   Út1Út2s          r)   rc   z_LogUniform._moment_raw_formulaN  sY   € Ø�AŠ:Ø—9‘9ÐØ�Y‰Y˜% %™-Ñ(¨5Ñ0ˆÜ�W‰W”R—V‘VœI e¨e¡m°U¸U±]ÓCÓDÓEˆØ�B‰wˆr*   )NNNN)rs   rt   ru   rv   r	   r   Ú	_a_domainÚ	_b_domainÚ_log_a_domainÚ_log_b_domainry   r   Ú_a_paramÚ_b_paramÚ_log_a_paramÚ_log_b_paramr|   Údefine_parametersr   r}   r~   r1   rò   r9   rc   r„   r…   s   @r)   rà   rà     s  ø„ ññ ¨¨C¨Ô1€IÙ¨¨c¨
Ô3€IÙ!¨c¨T°3¨KÔ8€MÙ!¨W°c¨NÔ;€MÙ¨¸|ÔL€Já˜c¨)¸[ÔI€HÙ˜c¨)¸ZÔH€HÙ! '°*Ø)6À
ôL€Lá! '°*Ø)6ÀôJ€Lá˜c¨*¸jÔI€Hà×Ñ Ô)Ø×#Ñ# LÔ1Ø× Ñ  ¨8Ô4á+¨L¸,ÓGÙ+¨H°hÓ?ðAÐà€Ià  D°¸Dö Góò'ör*   rà   c                   óx  ‡ — e Zd ZdZ ee ef¬«      Z edef¬«      Z edd¬«      Z e	ded¬«      Z
 e	d	ed
¬«      Z e	ded¬«      Zej                  e
«       ej                  e
e«        ee
e«      gZeZdddœˆ fd„
Zdd„Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zdge_         d„ Z!ˆ xZ"S )r   z±Uniform distribution.

    The probability density function of the uniform distribution is:

    .. math::

        f(x; a, b) = \frac{1}
                          {b - a}

    r   rá   rã   rå   ræ   rè   r   rä   ré   r   Nc                ó*   •— t        ‰| �  d||dœ|¤Ž y )Nrã   r/   r0   )r2   rá   rä   r'   r(   s       €r)   r1   zUniform.__init__p  ó   ø€ Ü‰ÑÐ,˜1 Ñ, VÓ,r*   c                 óJ   — ||z
  }|j                  t        |||¬«      «       |S )N)rá   rä   Úab)rð   rñ   ©r2   rá   rä   r  r'   s        r)   rò   zUniform._process_parameterss  s%   € Ø�‰UˆØ�‰”d˜Q !¨Ô+Ô,Øˆr*   c                óš   — t        j                  t        j                  |«      t         j                  t        j                  |«       «      S r"   )r5   ÚwhereÚisnanÚnanr6   ©r2   r   r  r'   s       r)   r4   zUniform._logpdf_formulax  s+   € Ü�x‰xœŸ™ ›¤R§V¡V¬b¯f©f°R«j¨[Ó9Ð9r*   c                óx   — t        j                  t        j                  |«      t         j                  d|z  «      S ©Nr   )r5   r	  r
  r  r  s       r)   r9   zUniform._pdf_formula{  s%   € Ü�x‰xœŸ™ ›¤R§V¡V¨Q¨r©TÓ2Ð2r*   c                ó¶   — t        j                  d¬«      5  t        j                  ||z
  «      t        j                  |«      z
  cd d d «       S # 1 sw Y   y xY w©NrO   rP   ©r5   rU   r6   ©r2   r   rá   r  r'   s        r)   r;   zUniform._logcdf_formula~  ó6   € Ü�[‰[ Ö)Ü—6‘6˜!˜a™%“=¤2§6¡6¨"£:Ñ-÷ *×)Ò)úó   —.AÁAc                ó   — ||z
  |z  S r"   r/   r  s        r)   r=   zUniform._cdf_formula‚  ó   € Ø�A‘˜‰|Ðr*   c                ó¶   — t        j                  d¬«      5  t        j                  ||z
  «      t        j                  |«      z
  cd d d «       S # 1 sw Y   y xY wr  r  ©r2   r   rä   r  r'   s        r)   r?   zUniform._logccdf_formula…  r  r  c                ó   — ||z
  |z  S r"   r/   r  s        r)   rA   zUniform._ccdf_formula‰  r  r*   c                ó   — |||z  z   S r"   r/   )r2   Úprá   r  r'   s        r)   rC   zUniform._icdf_formulaŒ  ó   € Ø�2�a‘4‰xˆr*   c                ó   — |||z  z
  S r"   r/   )r2   r  rä   r  r'   s        r)   rG   zUniform._iccdf_formula�  r  r*   c                ó,   — t        j                  |«      S r"   rÓ   )r2   r  r'   s      r)   rK   zUniform._entropy_formula’  s   € Ü�v‰v�b‹zÐr*   c                ó   — |d|z  z   S ©Nr   r/   r  s        r)   r^   zUniform._mode_formula•  ó   € Ø�3�r‘6‰zÐr*   c                ó   — |d|z  z   S r   r/   r  s        r)   r[   zUniform._median_formula˜  r!  r*   c                 ó.   — |dz   }||z  ||z  z
  ||z  z  S r  r/   )r2   rb   rá   rä   r  r'   Únp1s          r)   rc   zUniform._moment_raw_formula›  s&   € Ø�a‰iˆØ�3‘˜˜C™‘ C¨"¡HÑ-Ð-r*   c                 ó    — |dk(  r|dz  dz  S d S )Nr    é   r/   )r2   rb   r  r'   s       r)   ri   zUniform._moment_central_formulaŸ  s   € Ø  Aš:ˆr�1‰u�R‰xÐ/¨4Ð/r*   r    c                 ó„   — 	 |j                  |||¬«      d   S # t        $ r |j                  dd|¬«      |z  |z   cY S w xY w)Nr¼   r/   r   r   )ÚuniformÚOverflowError)r2   rp   rq   rá   rä   r  r'   s          r)   rr   zUniform._sample_formula¤  sO   € ð	=Ø—;‘;˜q !¨*�;Ó5°bÑ9Ð9øÜò 	=Ø—;‘;˜q !¨*�;Ó5°bÑ8¸1Ñ<Ò<ð	=ús   ‚ ™#?¾?)NNN)#rs   rt   ru   rv   r	   r   rù   rú   ry   r   rý   rþ   r|   r  r   r}   r~   r1   rò   r4   r9   r;   r=   r?   rA   rC   rG   rK   r^   r[   rc   ri   rƒ   rr   r„   r…   s   @r)   r   r   V  só   ø„ ñ	ñ ¨#¨¨s¨Ô4€IÙ¨¨c¨
Ô3€IÙ¨¸|ÔL€Já˜c¨)¸[ÔI€HÙ˜c¨)¸ZÔH€HÙ˜c¨*¸jÔI€Hà×Ñ Ô)Ø× Ñ  ¨8Ô4á+¨H°hÓ?Ð@ÐØ€Ià  Dö -óò
:ò3ò.òò.òòòòòòò.ò0ð '( SÐÔ"ö=r*   r   c                   ó‚   — e Zd Z edef¬«      Z edefd¬«      Z eded¬«      Z eded¬«      Z	 e
e«      gZe	Zd	„ Zy
)Ú_Gammar   r   ©FFræ   rá   )rì   é
   r   r   c                ól   — ||dz
  z  t        j                  | «      z  t        j                  |«      z  S r  )r5   r“   r   Úgamma)r2   r   rá   r'   s       r)   r9   z_Gamma._pdf_formula¶  s-   € Ø�Q˜‘U‰|œbŸf™f a R›jÑ(¬7¯=©=¸Ó+;Ñ;Ð;r*   N)rs   rt   ru   r	   r   rù   ry   r   rý   r|   r   r}   r~   r9   r/   r*   r)   r+  r+  «  sT   „ á¨¨C¨Ô1€IÙ¨!¨S¨¸^ÔL€Já˜c¨)¸YÔG€HÙ˜c¨*¸iÔH€Há+¨HÓ5Ð6ÐØ€Ió<r*   r+  c                   ó"  ‡ — e Zd ZdZ edefd¬«      Z edd¬«      Z edd¬«      Z	 e
ded	¬
«      Z e
ded¬
«      Z e
de	d¬
«      Z eee«      gZeZˆ fd„Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zddge_        d„ Zg d¢e_        ˆ xZS )r   zÚBinomial distribution with prescribed success probability and number of trials

    The probability density function of the binomial distribution is:

    .. math::

        f(x) = {n \choose x} p^x (1 - p)^{n-x}

    r   r,  ræ   )r   r   )r   rÙ   rå   rÙ   )r-  é   r   r  )g      Ð?g      è?r   )r   r-  c                ó*   •— t        ‰| �  d||dœ|¤Ž y )N©rÙ   r  r/   r0   )r2   rÙ   r  r'   r(   s       €r)   r1   zBinomial.__init__Ï  r  r*   c                ó0   — t        j                  |||«      S r"   )ÚscuÚ
_binom_pmf©r2   r   rÙ   r  r'   s        r)   Ú_pmf_formulazBinomial._pmf_formulaÒ  ó   € Ü�~‰~˜a  AÓ&Ð&r*   c                ó  — t        j                  |dz   «      t        j                  |dz   «      t        j                  ||z
  dz   «      z   z
  }|t        j                  ||«      z   t        j                  ||z
  | «      z   S r  )r   ÚgammalnÚxlogyÚxlog1py)r2   r   rÙ   r  r'   Úcombilns         r)   Ú_logpmf_formulazBinomial._logpmf_formulaÕ  so   € ô
 �O‰O˜A˜a™CÓ ¤G§O¡O°A°a±CÓ$8¼7¿?¹?È1ÈQÉ3ÈqÉ5Ó;QÑ$QÑRð 	ð œŸ™ q¨!Ó,Ñ,¬w¯©¸qÀ¹sÀQÀBÓ/GÑGÐGr*   c                ó0   — t        j                  |||«      S r"   )r5  Ú
_binom_cdfr7  s        r)   r=   zBinomial._cdf_formulaÞ  r9  r*   c                ój   — | j                  d||¬«      }t        j                  ||k  |||fd„ d„ «      S )Nr   r3  c                  óL   — t        j                  t        j                  | Ž «      S r"   )r5   r6   r5  rA  ©Úargss    r)   Ú<lambda>z*Binomial._logcdf_formula.<locals>.<lambda>æ  s   € œ"Ÿ&™&¤§¡°Ð!6Ô7r*   c                  óN   — t        j                  t        j                  | Ž  «      S r"   )r5   rª   r5  Ú	_binom_sfrD  s    r)   rF  z*Binomial._logcdf_formula.<locals>.<lambda>ç  s   € œ"Ÿ(™(¤C§M¡M°4Ð$8Ð#8Ô9r*   ©rC   ÚxpxÚapply_where©r2   r   rÙ   r  r'   Úmedians         r)   r;   zBinomial._logcdf_formulaá  s@   € ð ×#Ñ# C¨1°Ð#Ó2ˆÜ�‰˜q 6™z¨A¨q°!¨9Ù7Ù9ó
ð 	
r*   c                ó0   — t        j                  |||«      S r"   )r5  rH  r7  s        r)   rA   zBinomial._ccdf_formulaê  s   € Ü�}‰}˜Q  1Ó%Ð%r*   c                ój   — | j                  d||¬«      }t        j                  ||k  |||fd„ d„ «      S )Nr   r3  c                  óN   — t        j                  t        j                  | Ž  «      S r"   )r5   rª   r5  rA  rD  s    r)   rF  z+Binomial._logccdf_formula.<locals>.<lambda>ð  s   € œ"Ÿ(™(¤C§N¡N°DÐ$9Ð#9Ô:r*   c                  óL   — t        j                  t        j                  | Ž «      S r"   )r5   r6   r5  rH  rD  s    r)   rF  z+Binomial._logccdf_formula.<locals>.<lambda>ñ  s   € œ"Ÿ&™&¤§¡°Ð!5Ô6r*   rI  rL  s         r)   r?   zBinomial._logccdf_formulaí  s>   € Ø×#Ñ# C¨1°Ð#Ó2ˆÜ�‰˜q 6™z¨A¨q°!¨9Ù:Ù6ó
ð 	
r*   c                ó0   — t        j                  |||«      S r"   )r5  Ú
_binom_ppfr7  s        r)   rC   zBinomial._icdf_formulaô  r9  r*   c                ó0   — t        j                  |||«      S r"   )r5  Ú
_binom_isfr7  s        r)   rG   zBinomial._iccdf_formula÷  r9  r*   c                ó|   — t        j                  |dz   |z  «      }t        j                  |dk(  |dz
  |«      }|d   S )Nr   r/   )r5   Úfloorr	  )r2   rÙ   r  r'   Úmodes        r)   r^   zBinomial._mode_formulaú  s;   € ä�x‰x˜˜1™˜a™Ó ˆÜ�x‰x˜˜Q™  q¡¨$Ó/ˆØ�B‰xˆr*   c                óD   — |dk(  r||z  S |dk(  r||z  d|z
  ||z  z   z  S y r¨   r/   ©r2   rb   rÙ   r  r'   s        r)   rc   zBinomial._moment_raw_formula   s7   € à�AŠ:Ø�Q‘3ˆJØ�AŠ:Ø�Q‘3˜˜A™  !¡™Ñ$Ð$Ør*   r   r    c                óÔ   — |dk(  rt        j                  |«      S |dk(  r||z  d|z
  z  S |dk(  r||z  d|z
  z  dd|z  z
  z  S |dk(  r ||z  d|z
  z  dd|z  dz
  |z  d|z
  z  z   z  S y )Nr   r    r°   r±   é   )r5   rf   rZ  s        r)   ri   z Binomial._moment_central_formula	  s’   € à�AŠ:Ü—=‘= Ó#Ð#Ø�AŠ:Ø�Q‘3˜˜A™‘;ÐØ�AŠ:Ø�Q‘3˜˜A™‘;  A a¡C¡Ñ(Ð(Ø�AŠ:Ø�Q‘3˜˜A™‘;  Q q¡S¨1¡W¨a¡K°°Q±Ñ$7Ñ 7Ñ8Ð8Ør*   )r   r    r°   r±   )rs   rt   ru   rv   r
   r   Ú	_n_domainr	   Ú	_p_domainry   r   Ú_n_paramÚ_p_paramr|   r   r}   r~   r1   r8  r?  r=   r;   rA   r?   rC   rG   r^   rc   rƒ   ri   r„   r…   s   @r)   r   r   º  sË   ø„ ññ !¨A¨s¨8¸~ÔN€IÙ¨¸.ÔI€IÙ!¨HÀÔM€Já˜c¨)¸XÔF€HÙ˜c¨)¸\ÔJ€HÙ˜c¨*¸gÔF€Há+¨H°hÓ?Ð@ÐØ€Iô-ò'òHò'ò
ò&ò
ò'ò'òòð #$ Q ÐÔò
ò &2Ð×"Ð"r*   r   )#ÚsysÚnumpyr5   r   Ú
scipy._libr   rJ  Úscipyr   Úscipy.specialr   r5  Ú(scipy.stats._distribution_infrastructurer   r   r	   r
   r   r   r   Ú__all__r   r‰   r%   r   rà   r   r+  r   Úmodulesrs   Ú__dict__Ú_moduleÚ	dist_namerv   r/   r*   r)   Ú<module>rl     sÕ   ðÛ 
ã Ý å -Ý Ý (÷6÷ 6ñ 6ò 8€ôhDÐ#ô hDòV>ôK/�Vô K/ô\C1Ð%ô C1ôN?Ð(ô ?ôDR=Ð$ô R=ôj<Ð#ô <ôZ2Ð#ô Z2ð@ �+‰+�hÑ
×
(Ñ
(€Û€IÙ!.¨w°yÑ/AÓ!B€GˆIÑÕñ r*   